Seismic surface waves, also termed ground-roll or Rayleigh waves or Love waves, are confined to a region near the surface of the earth, and thus their propagation is dependent on the near surface elastic properties, particularly the shear-wave velocity as a function of depth from the surface. The shear-wave velocity is directly related to the stiffness of the soil as given by the soil shear-modulus. (The shear-wave velocity is the square root of the shear modulus divided by the density.) The shear wave velocity or shear modulus profile and other elastic characterization of the soil can be used directly for engineering or other purposes or can be used indirectly to improve geophysical prospecting below the soil or near-surface region. In addition to the shear modulus or wave velocity, the elastic attenuation or amplitude decay with distance is also useful information that can be used for both engineering and geophysical prospecting.
The soil shear wave velocity or modulus can be determined by inverting ground-roll dispersion (phase-velocity versus frequency) curves to obtain the earth's shear-wave velocity profile. Because of compaction effects, velocities are generally slower near the surface of the earth and increase with depth. Higher frequency components of the surface waves are confined near the surface and sample the slower soil layers. On the other hand, lower frequency components sample deeper, faster layers. Thus, the velocity of the surface wave changes with frequency, i.e. it is dispersive. In particular the velocity decreases with increasing frequency. The shape of the dispersion curve as a function of frequency can be compared to computed dispersion curves calculated for a layered velocity profile, and then the profile properties, i.e. layer thickness and shear modulus, can be updated to better match the measured dispersion curves. Layering causes resonance effects and the trapping of different modes of the ground roll. More precision can be obtained by inverting the dispersion curves for both the fundamental and higher-order modes of the ground roll.
After surface waves are transformed into depth profiles of the soil shear-wave velocity or shear modulus, shear wave attenuation or other property, the information can be used directly as an important engineering parameter for designing structures such as buildings and bridges. Other applications for the direct use of surface waves for near-surface characterization include estimating the earthquake site response, soil compaction control, mapping the shallow surface, estimating the strength of subsurface materials, pavement evaluation, finding buried cultural features or anomalies, evaluating voids around sewers, and finding the depth to bedrock. The near-surface velocity profiles can be used indirectly to improve the determination of the physical structure or physical property of deeper subsurface regions for hydrocarbon assessment or extraction. Because the near-surface, has low velocity and is heterogeneous, it has a large effect on seismic waves that pass through it and can limit the ability to determine the structure and properties of deep regions. The near-surface velocity profile can be used to make time corrections or static corrections for the seismic reflections from deeper zones or the velocity information can be used for imaging, migration or for inversion of the seismic data.
A problem with all prior art methods that utilize surface waves, Rayleigh waves or Love waves is that it is difficult to resolve or distinguish different dispersion curves for different surface-wave modes. One inherent difficulty arises from frequency and velocity uncertainty, and the inversion is compromised when the wrong mode is identified or incorrectly picked. A second difficulty arises from lack of knowledge about the source phase and uncertainties in changes in phase over 2π. In addition, all such methods average the surface-wave properties over the receiver spread distance used in the analysis, and this averaging limits resolution. Finally, the interference between modes and noise and the attenuation of surface waves can distort the seismic amplitudes making identification of individual dispersion curves difficult. Next, traditional methods for determining soil shear modulus or shear wave velocity are discussed in somewhat more detail.
Current methods to use surface waves for characterizing the soil shear modulus or wave velocity involve the acquisition of seismic data followed by two processing stages: (1) the measurement of dispersion curves as a function of frequency and (2) then the inversion of the dispersion curves to obtain the shear modulus as a function of depth. Similar methods may be used separately to derive properties other than the shear modulus such as attenuation properties. The methods to measure the dispersion curves differ largely in the number of sources and the number of receivers acquired. The earliest methods used one source and a single pair of receivers. Newer methods use one source and multiple receivers (on the order of 20 or more) spaced at regular intervals. Most methods use a compression source, which generate Rayleigh waves, but shear sources can also be used to generate Love waves. The method to use either wave type is the same.
Stage 1: Methods for a Pair of Receivers
The earliest uses of Rayleigh waves for characterizing the soil shear modulus are “steady state methods” involving use of a seismic vibrator to vibrate the earth with a single frequency or with a slowly varying frequency (U.S. Pat. No. 3,864,667 to Bahjat (1975)). At each frequency, the phase difference between the responses of two geophones is measured. From these measurements, the properties of the near surface between the receivers are inferred. Such measurements, however, take a long time to acquire. In the 1980's, the SASW (Spectral Analysis of Surface Waves) method was developed (Nazarian et al., “Use of spectral analysis of surface waves method for determination of moduli and thickness of pavement systems,” Transport. Res. Record 930, 38-45 (1983)). The method determines the dispersion curve by first calculating a cross power spectrum between the signals recorded by the two sensors and then unwrapping the phase.
Both the SASW method and the steady state method suffer from similar problems. Because only a pair of receivers is used at a time, it is hard to distinguish between the effects of the different surface wave modes and the effects of any recorded noise. The distance between the receivers and between the pair of receivers and the source are varied to minimize, but not eliminate, the effects of the higher order modes. An inherent problem with these measurements is ambiguity around factors of 2π in phase. The receivers must be close enough together so that the phase does not change by more than 2π. It is important to be able to distinguish between a phase change of Δ and a change of Δ+2π; the latter corresponds to a slower velocity. Sometimes, a few additional receivers are used to assist in phase unwrapping.
More recently, use has been made of the Wavelet Transform as a method to allow an improved isolation of a single ground-roll mode and to minimize the contributions from other modes as explained by Holschneider et al. in “Characterization of dispersive surface waves using continuous wavelet transforms,” Geophys. J. Int. 163, 463-478 (2005). The wavelet transform is a time-frequency transform that can allow better localization of the individual modes. The method reduces interference between modes, but noise is still a problem as is the 2π ambiguity in phase. Holschneider, et al. constructs a mathematical model of the surface-wave propagation effects in the wavelet transform domain and uses it to solve first for dispersion curves and then for attenuation curves for one mode at a time.
Stage 1: Multiple Receivers
The Multichannel Analysis of Surface Wave method (MASW) was developed by the Kansas Geological Survey. In this method 20-65 or more receivers are deployed and data recorded from one impulsive or vibratory source. (Park et al., “Multichannel analysis of surface waves,” Geophysics 64, 800-808 (1999); and Park et al., “Multichannel analysis of surface waves (MASW) active and passive methods,” The Leading Edge 26, 60-64 (2007)). The data are processed as a single shot gather, the amplitudes are normalized or scaled, and then are transformed to the frequency wavenumber (f−k) domain or to the frequency slowness (f−p) domain. The dispersion curves for one or more modes are then picked at the points of maximum amplitudes in the f−k or f−p domains. The dispersion curves for one or more modes are used in the subsequent inversion of near-surface properties (Beaty et al., “Repeatability of multimode Rayleigh-wave dispersion studies,” Geophyics 68 782-790 (2003)). The acquisition may be repeated with each new shot fired into a new receiver spread, and each shot gather separately analyzed to obtain the 1D near-surface velocity profile for each spread. Each 1D profile is then combined with an interpolation scheme to generate a 2D profile of the near surface.
The multichannel method is an improvement over the SASW method. One advantage is that the use of closely spaced receivers minimizes the 2π ambiguity of phase changes; however, it is impossible to estimate the source phase from a single gather (Hermann and Ammon, “Surface Waves, Receiver Functions, and Crustal Structure: Version 3.3,” in Computer Programs in Seismology, Saint Louis University, http:www.eas.slu.edu/People/RBHermann/CPS330.htl. (2004)). Its second advantage is that the transformation to f−k or f−p domains inherently involves a sum or stack over the traces, which improves frequency resolution and reduces problems with noise. However, the trade-off is a loss in lateral resolution; it is impossible to detect changes in velocity within the width of the spread. As in the two channel case, it is also important to pick the offset range to emphasize or deemphasize various modes (Xia et al., “Utilization of high-frequency Rayleigh waves in near-surface geophysics,” The Leading Edge 23, 753-759 (2004)). In addition, the receivers must be uniformly spaced close together to not alias the ground roll. Furthermore because the ground-roll amplitudes are heavily attenuated, they vary from trace to trace, and the sum distorts the amplitudes. Normalization or amplitude balancing is used, but it is still difficult to pick and distinguish multiple interfering ground roll modes. Lefebvre and Benhassen (U.S. Patent Application Pub. No. 2005/0143924 A1) teach use of the wavelet transform to improve the ability to distinguish different modes. Forbriger (“Inversion of shallow-seismic wavefields: I. Wavefield transformation,” Geophys. J. Int. 153, 719-734 (2003)) illustrates difficulties in picking multimodal dispersion curves and problems with the subsequent inversion when the dispersion curves are incorrectly picked or misidentified. Both Forbridger and Ryden and Park (“Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra,” Geophysics 71, R49-R58 (2006)) avoid picking dispersion curves and instead invert the f−p transform results directly. These methods involve a mathematical model of surface-wave propagation in the f−p domain, which involves several assumptions and approximations.
Stage 1: Multiple Receivers and Multiple Sources
The simultaneous use of multiple source locations and multiple receivers to obtain laterally varying phase velocity curves is discussed by Ernst et al. in “Tomography of dispersive media,” J. Acoust. Soc. Am. 108, 105-115 (2000) and in “Removal of scattered guided waves from seismic data,” Geophysics 67, 1240-1248 (2002). The application is not for near-surface characterization, but instead for mitigation of scattered ground-roll for oil exploration seismic applications. Their process includes a cascade of operations. They first invert for a laterally changing phase velocity as a function of frequency using a tomography method based on generalized travel times. They assume that lateral changes are small and that they can obtain isolation of one mode in a time window. This latter assumption requires that the source and receivers are sufficiently far apart that the modes are well separated in time, but because of the strong attenuation of surface wave modes, this is difficult or impossible to achieve with data acquired for near-surface characterization. The use of generalized traveltimes involves computation of the derivative of the phase of the data, and problems of phase ambiguity in the determination of ground-roll phase velocity are increased.
Stage 1: Attenuation Versus Frequency Curves
While most of the prior art concentrates on phase-velocity dispersion curves, the use of attenuation curves as a function of frequency is discussed by Xia et al. (op. cit.). The quality factor (Q) as a function of depth along with the shear modulus is also an important engineering quantity, but the inversion of data for attenuation has less stability. Generally, the assumption is made that attenuation is independent of frequency (Ernst et al., “Removal of scattered guided waves from seismic data,” Geophysics 67, 1240-1248 (2002); and Kulesh et al., “Modeling of Wave Dispersion Using Continuous Wavelet Transforms II: Wavelet Based Frequency-Velocity Analysis,” Pure & Applied Geophysics 165, 255-270 (2008)). However, for surface waves of use for near-surface characterization, this assumption is limiting. Because the attenuation typically decreases for increasing soil depth, the attenuation of surface waves must also decrease as a function of frequency in the same manner that the phase velocity is dispersive.
Stage 2: Inversion of Dispersion Curves for Near-Surface Velocity Profiles
There are a number of algorithms available to solve for the near-surface velocity profile from dispersion curves, but the success of all such methods depend on the accuracy of the input dispersion curves. The inversion is a nonlinear model optimization problem in which the model is the near-surface velocity profile. Parameters include layer depths and layer shear modulus. The algorithms include linearized least squares inversion, Levenberg Marquardt, quasi-Newton, and more recently simulated annealing (Beaty et al., “Simulated annealing inversion of multimode Rayleigh wave dispersion curves for geological structure,” Geophys. J. Int. 151, 622-631 (2002)). Available software include freeware (Hermann and Ammon, “Surface Waves, Receiver Functions, and Crustal Structure: Version 3.3,” in Computer Programs in Seismology, Saint Louis University, http:www.eas.slu.edu/People/RBHermann/CPS330.htl. (2004)), and commercial software (SeisOpt® ReMi™, http:www.optimsoftware.com; and Kansas Geological Survey: http:/www.kgs.ku.edu/software/surfseis./index.html.).
There remains a need for an improved method for transforming surface waves into depth profiles of near-surface properties by attaining high resolution, laterally varying, multi-mode dispersion and attenuation curves for input into near-surface characterization inversion. In particular, the method should minimize ambiguities in the source phase. The present invention satisfies this need.